Forward Analysis of 5 DOF Robot_Manipulator

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Eng. & Tech. Journal , Vol.32,Part (A), No.3, 2014

617

Forward Analysis of 5 DOF Robot Manipulator and Position

Placement Problem for Industrial Applications

Alaa Hassan Shabeeb

Production and Metallurgy Engineering Department, University of Technology/Baghdad

Email:[email protected]

Dr.Laith A. Mohammed

Production and Metallurgy Engineering Department, University of Technology/Baghdad

Received on:29/5/2013 & Accepted on:3/10/2013

ABSTRACTIn this paper, a forward kinematics problem is concerned with the relationship between the

individual joint of robot arm and the position and orientation of the tool or end-effector. Thestandard Denavit_Hartenberg(D-H) analytical scheme is applied to building mathematicalmodeling to predict, simulate and recovering the end-effector location (position and orientation)

placement of 5DOF R5150 Robot manipulator for different joint variables, the basic challenge

associated with the R5150 arm is the limited information available on its governing control modelfor position placement. Two ways by which control can be effected on R5150 arm, this robot can

be programmed by using either a hand-held terminal (teach pendant) or a RoboCIM simulationsoftware. The non-versatility of this control software is seen in the non-availability of a

programmable environment by users. The user interface of RoboCIM allows for numeric

keyboard inputs such that each input results in the orientation of a specific joint by a margin

equivalent to the input. The relationship between the keyboard inputs and joint motion of the armis not feasible to the users. The proposed D-H scheme as presented herein has successfullyreproduced the end-effecter position of the Lab_volt R5150 Robot arm with marginal differencesfor different experimental trials. The simulation of robot arm forward kinematics is performed

through MATLAB. The adopted modeling is validated in the physical behaviors in determineposition of robot arm.

Keywords: Forward Kinematics; D-H Concept; Lab Volt R5150 RobotArm.

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Eng. & Tech. Journal , Vol.32,Part (A), No.3, 2014 Forward Analysis of 5 DOF Robot Manipulator and Position Placement Problem for Industrial Applications

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executive mechanism, and solved the problem using (D-H) transformation. The three dimensional

model of the arm was created by Pro/E. Baki Koyuncu, and Mehmet Gzel [9], presentedmathematical modeling and kinematic analysis of a low Cost Robot arm (Lynx-6). Robot arm was

mathematically modeled with (D-H) method. Forward and Inverse Kinematics solutions weregenerated and implemented by the developed software. Also K. M. Mohanasundaram et al.[10]

presented a novel approach used for solving the forward kinematics mathematical model ofSCORBOT ER V PLUS in its work space for various set of joint parameters. The obtained resultswere validated with ROBOCELL 3D graphic software and also using CAD 3D model in

AutoCAD 2007. A system based on the theory of computer aided geometric method wasproposed. The entire system has been modeled using LabVIEW2011.Tahseen F. Abbas[11],presented a direct kinematics modeling of 5 DOF stationary articulated robot arm which is usedfor educational tasks, the Denavite Hartenberg (D-H) model of representation is used to modelrobot links and joints in this paper. It utilizes Matlab software as the tools for manipulation and

testing. The adopted modeling solution was found to be identical with the physical behaviors.

ROBOT DESCRIPTIONR5150 Robot manipulator used in the work is a 5 DOF robot arm manipulator R5150 by

LabVolt Inc. It is a five articulated coordinate robotic manipulator that uses stepper motors for

joint actuators, and its motion are controlled by RoboCIM software. R5150 Robot manipulatorhas a stationary base, shoulder, elbow and wrist in corresponding with human arm joints (noyaw), each of these joints except the wrist has a single DOF. Wrist can move into planes (roll,

pitch), this making the end-effector move flexible in terms of object manipulation.

FORWARD KINEMATICS ANALYSIS OF THE LAB_VOLT R5150 ROBOT

MANIPULATOR

The study location placement problem of robot arm in this work involves the analysis andverification of the D-H method as applied to the 5 DOF Lab_Volt Robot R5150 robot

manipulator. The application of this method, including the construction of the joint/link parametertable allow to determine the corresponding 4 x 4 homogeneous transformation matrices for therobot arm manipulator. The analysis addressed in the forward kinematics analysis of Lab_VoltR5150 robot arm, while the verification and application of results conducted with the actual robotmanipulator to implement end-effector position analysis. The analysis involves three major steps:

1) An assignment of a coordinate frame to each controlled joint axis and to the end-effector.2) Construction of the joint/link parameter Table.3) Use the parameters in each row of the parameter table to generate each of the five 4 x 4

coordinate transformation matrices, T(shoulder, base), T(elbow, shoulder), T(pitch, elbow),T(roll, pitch) and T(tool, roll).Then, as an added step, determine T (tool, reference), where,

T(tool, reference(base)) =T(shoulder, base) x T(elbow, shoulder) x T(pitch, elbow) x T(roll, pitch)x T(tool, roll).

The direct or forward kinematics problem is to specify a set of values for the joint variablesand then calculate the 4 x 4 matrix, T (tool, reference). The fourth column of this matrix definesthe coordinates of the origin of the tool frame (point, P) referred to the reference frame. The third

column of this matrix defines the projections of the approach vector (z or a axis of the tool frame)onto the x, y, and z axes of the reference frame. The second column of this matrix defines the

projections of the orientation vector (y or o axis of the tool frame) onto the x, y and z axes of the


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reference frame. Finally, the first column of this matrix defines the projections of the normal axis

(x or n axis of the tool frame) onto the x, y and z axes of the reference frame.

D-H PROCEDURE ADOPTED

The steps to get the position using D-H procedure are finding the Denavid-Hartenberg (D-H)

parameters, building matrices, and calculating T matrix with the coordinate position which isdesired. It is a method of assigning coordinate frames to the different joints of a roboticmanipulator. The following ten steps denote the systematic derivation of the D-H parameters as

follows:1. Label each axis in the manipulator with a number starting from (0) as the base to (n) as theend-effector. Every joint must have an axis assigned to it.2. Set up a coordinate frame for each joint. Starting with the base joint, set up a right handedcoordinate frame for each joint. For a rotational joint, the axis of motion of the i thjoint is always

along (Zi}1). If the joint is a prismatic joint, Z( i}1)should point in the direction of translation.3. The (Xi) axis is normal to (Zi}1) axis, and always point away from it.4. (Yi) should be directed such that a right-handed orthonormal coordinate frame is created.5. For the next joint, if it is not the end-effector frame, steps 24 should be repeated.

6. For the end-effector, the (Zn) axis should point in the direction of the end-effector approach.7. Joint angle (~i) is the rotation about (Zi}1) axis to make (X i}1) axis parallel to (Xi) axis.8. Twist angle ( i) is the rotation about (Xi) axis to make (Zi }1) axis parallel to (Zi) axis.9. Link length (ai) is distance measured along (Xi) axis from the point of intersection of (Xi) axiswith (Zi}1) axis to the origin of frame (i)10. Link offset (di) is distance measured along (Zi }1) axis from the origin of frame (i-1) tointersection of (Xi) axis with (Zi-1) axis.Applying the D-H algorithm, A D-H coordinate system of the robot manipulator is shown in

Figure (1). The parameters of links are given in Table (1).

TRANSFORMATION MATRIX

After establishing (D-H) coordinate system for each link, a homogeneous transformation

matrix can easily be developed considering frame {i-1} and frame {i} transformation consistingof four basic transformations as shown in Table (2). There four parameters are respectively jointangle ~i, link offset di , link length ai and the twist angle i ,So, the link transformation matrix between coordinate fram i-1 and coordinate frame i has thefollowing form;

=

1000

5

0

zzzz

yyyy

xxxx

paon

paon

paon

T

),().,().,().,.(iiiii

xRotaxTransdzTranszRotT =


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According to (H-D) method [12], we can get the homogenous transformation matrix of R5150robot manipulator as follows.

=

1000

0100

0

0

3333

3333

3

2sacs

casc

T

=

1000

100

00

00

5

55

55

5

4

d

cs

sc

T

=

1000

0100

0

0

2222

2222

2

1

sacs

casc

T

=

1000

1000

00

00

11

11

1

0

d

cs

sc

T

=

1000

0010

00

00

44

44

4

3

cs

sc

T

=

=

1000

cossin0

sin.sin.coscos.cossin

cos.sin.sincos.sincos

1000

0cossin0

0sincos0

0001

1000

100

0010

001

1000

0100

00cossin

00sincos

iii

iiiiiii

iiiiiii

i

ii

ii

i

i

ii

ii

i

d

a

a

T

d

a

T


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Therefore the transformation matrix between tool frame and the base frame is obtained as follow:

Where

)()(,, 322332231111 +=+=== SinSandCosCSinSCosC

The general position vector (the tool-tip position) of R5150 Robot manipulator is given by

++

++

++

=

2345222331

2345222331

2345222331

)(

)(

cdsasad

sdcacas

sdcacac

P

P

P

z

y

x

The previous forward kinematics solution can be used for modeling the position of each jointof the manipulator as it moves.

=

10

0

0

Base ,

=

1

0

0

1d

Shoulder ,

+

=

1

221

122

212

Sad

SCa

CCa

Elbow ,

These models have been used to simulate the positional coordinates of each joint of the robot

manipulator while it moves to a desired target.

VERIFICATION OF MATHEMATICAL MODEL USING MATLAB 10.0 PROGRAMM

WITH ROBOCIM SOFTWARE

The simulation results as presented are for the forward kinematic analysis of the Lab_volt

R5150 Robot as modeled using the (D-H) concept. Simulations were conducted using MatlabRobotics Toolbox on an Intel (R) CPU T2080 @ 0.99GHz, 1.00GB Memory (RAM), 32bit

5

4

4

3

3

2

2

1

1

0

5

0 TTTTTT =

++

++

+++

=

1000

)(

)(

234522233123452345234

2345222331234151523415152341

2345222331234152341515152341

5

0

cdsasadcsscs

sdcacasssccscssccss

sdcacacscscccsssccc

T

++

++

++

=

1

)(

)(

2345233221

2345233221

2345233221

CdSaSad

SdCaCaS

SdCaCaC

tipTool

++

+

+

=

1

233221

2313212

2313212

SaSad

CSaCSa

CCaCCa

Wrist


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Operating System. The Matlab Robotics Toolbox was used to represent the graphical simulation

of the serial link manipulator. The variables ~1, ~2, ~3, ~4, and ~5 respectively represent the jointaxes 0 through 4.Kinematics equations from the overall transformation matrix were developed

using the Matlab R 10.0. An algorithm has been developed to generate the forward kinematicsequations and calculate the robot Manipulator tool position and orientation in terms of jointangles and its output is compared with Robot software (which is the simulate program suppliedwith the robot system) for many sets of joint parameters. The result of end-effecters positionfrom Matlab simulation was then compared with experimental result generated from inbuilt

Robot software (RoboCIM). For different keyboard values entered on the RoboCIM software, thecorresponding joint angles, simulation and experimental positions for the end-effecter are

presented as shown in the Figures (2) through Figure (13).

A. Experiment No :1

A summing the following values are entered (for the lab_volt R5150 arm joint axes) on the

RoboCIM software, the resulting joint angles are as stated in belowJoint 1: axis 0 ~1= 0 ; Joint 2 : axis 1 ~2= 130; Joint 3 : axis 2 ~3= -130;

Joint 4 : axis 3 ~4= 90; axis 4 ~5= 90;The analytical values using DH model were given as Px = 182.870, Py = 0, Pz = 401.098 all in

millimeters. The forward kinematics matrix from the DH model is given as:

5

0T =

1000

48.401010

0001

87.182100

The resulting end-effecters position as plotted on the Matlab Robotics Toolbox is as shown in

Figure (2).while The variable Px,Py,Pz as given by the RoboCIM are Px = 182.55 , Py = 0 , P z = 401.48

all in millimeters and The resulting end-effecters position as plotted on the RoboCIM is asshown in Figure (3) and Physical Configuration (Real) of the Robot Manipulator for the Case oneas shown in Figure (4).

B. Experiment No :2


RoboCIM software, the resulting joint angles are as stated in belowJoint 1: axis 0 ~1= 9 ; Joint 2 : axis 1 ~2= 28; Joint 3 :

axis 2 ~3= -89.59; Joint 4: axis 3 ~4= 9.29; axis 4 ~5= 0;The analytical values using DH model were given as Px = 165.109, Py = 26.1507, P z = 107.3065all in millimeters. The forward kinematics matrix from the DH model is given as:


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5

0T =

1000

107.30650.6115-00.7912-

26.15070.1238-0.9877-0.0957

165.1090.7815-0.15640.6040


Figure (5).while The variable Px,Py,Pz as given by the RoboCIM are Px = 165.29 , Py = 26.18 , P z =

107.10 all in millimeters and The resulting end-effecters position as plotted on the RoboCIM is

as shown in figure 6 and Physical Configuration (Real) of the Robot Manipulator for the Casetwo as shown in Figure (7).

C.

Experiment No :3


RoboCIM software, the resulting joint angles are as stated in belowJoint 1: axis 0 ~1= 45 ; Joint 2 : axis 1 ~2= 14.78; Joint 3 : axis 2 ~3=

20.48; Joint 4 : axis 3 ~4= 54.73 axis 4 ~5= 45.02;The analytical values using DH model were given as Px = 320.924, Py = 320.924, P z =

413.685 all in millimeters. The forward kinematics matrix from the DH model is given as:

5

0T =

1000

413.68520.0002-0.7074-0.7069

320.92470.70710.4999-0.5001-

320.92470.70710.499710.5003

The resulting end-effecters position as plotted on the Matlab Robotics Toolbox is as shown inFigure (8).

while The variable Px,Py,Pz as given by the RoboCIM are Px = 321.20 , Py = 321.20 , P z =414.10 all in millimeters and The resulting end-effecters position as plotted on the RoboCIM isas shown in Figure (9) and Physical Configuration (Real) of the Robot Manipulator for the Case

three as shown in Figure (10).

D. Experiment No :4

A summing the following values are entered (for the lab_volt R5150 arm joint axes) on theRoboCIM software, the resulting joint angles are as stated in below

Joint 1: axis 0 ~1= -24; Joint 2: axis 1 ~2= 15; Joint 3 : axis 2 ~3=-60;Joint 4: axis 3 ~4= 88; axis 4 ~5= 90;The analytical values using DH model were given as Px = 362.0436, Py = -161.1922, P z =

86.2697 all in millimeters. The forward kinematics matrix from the DH model is given as:


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5

0T =

1000

86.26970.7314-0.6820-0

161.1922-0.2774-0.29750.9135-

362.04360.62300.6681-0.4067-


Figure (11) while The variable Px,Py,Pz as given by the RoboCIM are Px = 362.35 , Py = -161.33, P z = 86.04 all in millimeters and The resulting end-effecters position as plotted on theRoboCIM is as shown in Figure (12) and Physical Configuration (Real) of the Robot Manipulator

for the Case four as shown in Figure (13).

RESULT AND CONCLUSION

The forward kinematics model predicated on Denavit Hardenberg's (D-H) analytical schemefor robot arm position analysis is investigated. The mathematical model is prepared and solved

for position and orientation of the end-effector by preparing a forward analysis algorithmprogrammed in Matlab 10. The developed model aims to predict and recover the end-effectersposition of lab_volt R5150 Robot manipulator for different joint variables. The simulationresults as presented are for the forward kinematic analysis of the robot manipulator as modeledusing the DH concept. Simulations were conducted using Matlab Robotics Toolbox. The

variables ~1 ~2 ~3 ~4 and ~5 respectively represent the joint axes 0 through 4. The resulting endeffectors position as plotted on the Matlab simulation as shown in Figures (2, 5, 8, 11), and thencompared with experimental results generated from inbuilt R5150 Robot software (RoboCIM)shown in Figures (3, 6, 9, 12). When position of target compared, there is a reasonable correlation

between the experimental readings obtained from the R5150 robot manipulator position analysis

software and the results obtained from the analytical modeling process. There is a high indicationthat our utmost goal of building a robot arm with a position placement scheme predicated on theDH concept would be realistic. Using simulation process, it can directly observe of physical

behaviors the robot motion and get the required data in the graphic form. Therefore, virtual

performance of the robot manipulator can be tested in the conceptual design stage so as toimprove the design performance, reduce design cost and decrease product development time.

REFERENCES[1]. Mark W. Spong, "Robot Modeling and Control", 1st Edition, John Wiley & Sons, 2005.

[2].Mittal R.K. & Nagrath I.J, "Robotics & Control", First Edition, Tata McGraw-Hill PublishingCo. Ltd., pp 70-107,2006.

[3].Niku Saeed B, "Introduction to Robotics Analysis, Systems & Applications", First Edition,

Pearson Education Pvt. Ltd, 2003.[4].Schiling Robert J, Fundamentals of Robotics, Prentice-Hall of India Pvt. Lid, pp 25-76,

2009.[5]. John J.Craig, Introduction to Robotics. 2nd ed. Pearson Education International, 2005.[6].Corke,P.I., "A Robotics Toolbox for MATLAB", Ninth release, Springer Publishing Co,September 2011.

[7].H.S. Lee and S.L. Chang, "Development of a CAD/CAE/CAM system for a robot


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manipulator" Journal of Materials Processing Technology, Vol 140, p.p. 100104, 2003.

[8]. Jun Xie, Jun Zhang and Jie Li, Mechanism Design and Kinematics Simulation of MassageMechanical Arm, Applied Mechanics and Materials Volumes. 101-102 ,PP 279-28, 2012.

[9]. Baki Koyuncu, and Mehmet Gzel,"Software Development for the Kinematic Analysis of aLynx 6 Robot Arm ", World Academy of Science, Engineering and Technology, 2007.

[10].K. M. Mohanasundaram , N. Godwin Raja Ebenezer and C. Krishnaraj. "ForwardKinematics Analysis of SCORBOT ER V Plus using LabVIEW" .European Journal of ScientificResearch, Vol.72 No.4, pp. 549-557, 2012.

[11].Dr.Tahseen Fadhil Abbas , Forward Kinematics Modeling of 5 DOF Stationary ArticulatedRobot". Eng. & Tech. Journal, Vol.31,pp.500-513, No.3, 2013.

[12].J J. Denavit, R.S. Hartenberg, A kinematics Notation For Lower-Pair Mechanisms BasedOn atrices ,ASME Journal of Applied Mechanics, vol. 22, pp. 215221, 1955.[13]. Alaa H. Shabeeb., "Path Planning of Robot Manipulator Using Bezier Technique ", M.Sc,

thesis, Department of Production Engineering and Metallurgy, University of Technology, 2013.

Y3

ToolWaistTool Roll

d5

Z5

Y5

X5

Z3

X3

Origins coincident

4

Y4

Z4

X4

5

a3 a2Elbow Shoulde

Tool pitch

d1

Z2

X2

Y2

3

1

Y0

X0

Z

0

Z1

X1

Y12

Figure (1) link coordinates of a 5DOF Robot manipulator [13].


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Figure( 2) Matlab Simulation Plot

for Experiment one.

Figure (3) RoboCIM Simulation

Plot for Experiment one.Figure (4): Physical Configuration (Real) of the

Robot Manipulator for the Experiment one

Figure(5) Matlab Simulation Plot

for Experiment two.Figure(6) RoboCIM Simulation Plot

for Experiment two.Figure (7) Physical Configuration (Real) of the

Robot Manipulator for the Experiment two.

Figure8: Matlab Simulation Plot

for Experiment threeFigure 9: RoboCIM Simulation Plot for

Experiment threeFigure 10: Physical Configuration (Real) of theRobot Manipulator for the Experiment three


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Table (1) link parameter of the robot manipulator [13].

Joint

i

joint

namei id

(mm)

ia

( mm)

i range motion

1 base 1 255.5 0 90 -185 to +153 rotates the body

2 shoulder 2 0 190 0 -32 to +149 raises and lowers(upper arm)

3 elbow 3 0 190 0 -147 to +51 raises and lowers(forearm)

4 wrist pitch 4 0 0 90 -5 to 180 raises and lowers(gripper)

5 wrist roll 5 115 0 0 360 rotates the gripper

Table (2) Transferring from frame i-1 to frame i

Operation Description

T1 A rotation about zi-1 axis by an angle ~i.

T2 Translation along zi-1 axis by distance di.

T3 Translation by distance ai along xi axis

T4 Rotation by angle i about xi axis

Figure(11) Matlab Simulation Plot

for Experiment four.

Figure (12) RoboCIM Simulation Plot

for Experiment four.

Figure (13) Physical Configuration (Real) of theRobot Manipulator for the Experiment four.

Forward Analysis of 5 DOF Robot_Manipulator

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